Electron wave-particle duality

The essential features of the particle-wave duality are clearly illustrated by Young s double-slit experiment. In order to explain all of the observations of this experiment, light must be regarded as having both wave-like and particlelike properties. Similar experiments on electrons indicate that they too possess both particle-like and wave-like characteristics. The consideration of the experimental results leads directly to a physical interpretation of Schrodinger s wave function, which is presented in Section 1.8. 

Having now demonstrated that a moving electron can be considered as a wave, it remained for an equation to be developed to incorporate this revolutionary idea. Such an equation was obtained and solved by Erwin Schrodinger in 1926 when he made use of the particle-wave duality ideas of de Broglie even before experimental verification had been made. We will describe this new branch of science, wave mechanics, in Chapter 2. 

However, in the sodium atom, An = 0 is also allowed. Thus the 3s —> 3p transition is allowed, although the 3s —> 4s is forbidden, since in this case A/ = 0 and is forbidden. Taken together, the Bohr model of quantized electron orbitals, the selection rules, and the relationship between wavelength and energy derived from particle-wave duality are sufficient to explain the major features of the emission spectra of all elements. For the heavier elements in the periodic table, the absorption and emission spectra can be extremely complicated - manganese and iron, for example, have about 4600 lines in the visible and UV region of the spectrum. 

During this same period de Broglie s brother Maurice was studying experimental physics, and he was particularly interested in x rays. The brothers frequently discussed x rays, and their dual nature (both wavelike and particle-like behavior) suggested to Louis that this same particle-wave duality might also apply to particles such as electrons. 

If one has differentiated information about elementary particles like protons, neutrons and electrons which connect to questions of chemical bonding, misconceptions can arise which mix bent water molecules or the 11-protons nucleus of a sodium atom with macroscopic characteristics of matter (see also Sect. 4.3). Since electrons are not ordinary basic particles of matter in the sense of atoms, ions and molecules, but are recognized more as charged clouds, orbital or through the particle-wave duality, the mixing of macroscopic and sub-microscopic characteristic properties should be avoided more carefully. 

The size-evolution of the physical properties from atom to bulk might also be related in part to the variation of the surface-to-volume ratio. In addition to these classical effects, however, the quantum mechanical properties of the electrons play an equally important role. These so-called quantum-size effects can be understood most simply by realizing that a conduction electron in a metal has both particle-and wave-like properties, according to the famous particle-wave duality of quantum mechanics. Treated as a wave-phenomenon, the electron in a metal has a wavelength of one to a few nanometers. The wave-character of the electron will... 

The wave function is used to describe electrons around the nucleus of an atom because electrons can be difBacted. Diffiaction is usually associated with electromagnetic radiation (light), but electrons also produce diffraction patterns. This means that electrons also exhibit particle-wave duality. In some instances, electrons are treated as particles in other instances, they are treated as waves. 

Quantum mechanics is the theory that captures the particle-wave duality of matter. Quantum mechanics applies in the microscopic realm, that is, at length scales and at time scales relevant to subatomic particles like electrons and nuclei. It is the most successful physical theory it has been verified by every experiment performed to check its validity. It is iso the most counter-intuitive physical theory, since its premises are at variance with our everyday experience, which is based on macroscopic observations that obey the laws of classical physics. When the properties of physical objects (such as solids, clusters and molecules) are studied at a resolution at which the atomic degrees of freedom are explicitly involved, the use of quantum mechanics becomes necessary. 

We are used to thinking of electrons as particles. As it turns out, electrons display both particle properties and wave properties. The French physicist Louis de Broglie first suggested that electrons display wave-particle duality like that exhibited by photons. De Broglie reasoned from nature s tendency toward symmetry If things that behave like waves (light) have particle characteristics, then things that behave like particles (electrons) should also have wave characteristics. 

Electrons have wave-particle duality, whereas golf balls do not. 

The Lewis model of the chemical bond assumes that each bonding electron pair is located between the two bonded atoms—it is a localized electron model. However, we know from the wave-particle duality of the electron (Sections 1.5-1.7) that the location of an electron in an atom cannot be described in terms of a precise position, but only in terms of the probability of finding it somewhere in a region of... 

The LEED experiment relies on the duality of electrons, which have both particle and wave character. Electrons of primary energy, p, somewhere in the minimum of the mean-free path curve (Eig. 4.7) possess a wavelength, 1, that is comparable with the distance between atoms in a lattice ... 

Erwin Schrodinger (1887-1961 Nobel Prize for physics 1932) transferred the concept of wave-particle duality of matter developed by L. V. de Broglie for electrons to the whole atom and thus developed wave mechanics. The Schrodinger equation allows a description of orbitals as the probability of the location of the electrons. Wave mechanics represented a significant development, but were subsequently shown to be insufficient. 

Schrodinger equation valence electrons wave function wavelength, X wave mechanical model wave-particle duality of nature... 

The electron, discovered by J. J. Thomson in 1895, was first considered as a corpuscule, a piece of matter with a mass and a charge. Nowadays things are viewed differently. We rather speak of a wave-particle duality whereby electrons exhibit a wavelike behavior. But, in Levine s own words [45], quanmm mechanics does not say that an electron is distributed over a large region of space as a wave is distributed it is the probability patterns (wavefunctions) used to describe the electron s motion that behave like waves and satisfy a wave equation. 

Electron diffraction In 1924, de Broglie postulated his principle of wave-particle duality. Just as radiation displays particle-like characteristics, so matter should display wave-Uke characteristics. It followed, therefore, from eqs (22) and (2.7) that a particle with energy, E, and momentum, p, has associated with it an angular frequency, , and wave vector, k, which are given by... 

Describe how the photoelectric effect and electron diffraction demonstrate the particle-like character of radiation and the wave-like character of particles respectively. Show how Heisenberg s uncertainty principle embraces the concept of wave particle duality. 

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